\chapter[Geometry \\ \textnormal{\emph{Lectured in Lent \oldstylenums{2022} by \textsc{Prof.\ I.\ Smith}}}]{Geometry}
\emph{\Large Lectured in Lent \oldstylenums{2022} by \textsc{Prof.\ I.\ Smith}}

This course serves as an introduction to the modern study of surfaces in geometry.
A surface is a topological space that locally looks like the plane.
The notions of length and area on a surface are governed by mathematical objects called the fundamental forms of the surface at particular points.
We can use integrals to work out exact lengths and areas.
We study various spaces, including spaces of constant curvature, such as the plane, spheres, and hyperbolic space.

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